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• Ball to Ball Collision - Detection and Handling

  - by Simucal

  With the help of the Stack Overflow community I've written a pretty basic-but fun physics simulator. You click and drag the mouse to launch a ball. It will bounce around and eventually stop on the "floor". My next big feature I want to add in is ball to ball collision. The ball's movement is broken up into a x and y speed vector. I have gravity (small reduction of the y vector each step), I have friction (small reduction of both vectors each collision with a wall). The balls honestly move around in a surprisingly realistic way. I guess my question has two parts: What is the best method to detect ball to ball collision? Do I just have an O(n^2) loop that iterates over each ball and checks every other ball to see if it's radius overlaps? What equations do I use to handle the ball to ball collisions? Physics 101 How does it effect the two balls speed x/y vectors? What is the resulting direction the two balls head off in? How do I apply this to each ball? Handling the collision detection of the "walls" and the resulting vector changes were easy but I see more complications with ball-ball collisions. With walls I simply had to take the negative of the appropriate x or y vector and off it would go in the correct direction. With balls I don't think it is that way. Some quick clarifications: for simplicity I'm ok with a perfectly elastic collision for now, also all my balls have the same mass right now, but I might change that in the future. In case anyone is interested in playing with the simulator I have made so far, I've uploaded the source here (EDIT: Check the updated source below). Edit: Resources I have found useful 2d Ball physics with vectors: 2-Dimensional Collisions Without Trigonometry.pdf 2d Ball collision detection example: Adding Collision Detection Success! I have the ball collision detection and response working great! Relevant code: Collision Detection: for (int i = 0; i < ballCount; i++) { for (int j = i + 1; j < ballCount; j++) { if (balls[i].colliding(balls[j])) { balls[i].resolveCollision(balls[j]); } } } This will check for collisions between every ball but skip redundant checks (if you have to check if ball 1 collides with ball 2 then you don't need to check if ball 2 collides with ball 1. Also, it skips checking for collisions with itself). Then, in my ball class I have my colliding() and resolveCollision() methods: public boolean colliding(Ball ball) { float xd = position.getX() - ball.position.getX(); float yd = position.getY() - ball.position.getY(); float sumRadius = getRadius() + ball.getRadius(); float sqrRadius = sumRadius * sumRadius; float distSqr = (xd * xd) + (yd * yd); if (distSqr <= sqrRadius) { return true; } return false; } public void resolveCollision(Ball ball) { // get the mtd Vector2d delta = (position.subtract(ball.position)); float d = delta.getLength(); // minimum translation distance to push balls apart after intersecting Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d); // resolve intersection -- // inverse mass quantities float im1 = 1 / getMass(); float im2 = 1 / ball.getMass(); // push-pull them apart based off their mass position = position.add(mtd.multiply(im1 / (im1 + im2))); ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2))); // impact speed Vector2d v = (this.velocity.subtract(ball.velocity)); float vn = v.dot(mtd.normalize()); // sphere intersecting but moving away from each other already if (vn > 0.0f) return; // collision impulse float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2); Vector2d impulse = mtd.multiply(i); // change in momentum this.velocity = this.velocity.add(impulse.multiply(im1)); ball.velocity = ball.velocity.subtract(impulse.multiply(im2)); } Source Code: Complete source for ball to ball collider. Binary: Compiled binary in case you just want to try bouncing some balls around. If anyone has some suggestions for how to improve this basic physics simulator let me know! One thing I have yet to add is angular momentum so the balls will roll more realistically. Any other suggestions? Leave a comment!

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• RK4 Bouncing a Ball

  - by Jonathan Dickinson

  I am trying to wrap my head around RK4. I decided to do the most basic 'ball with gravity that bounces' simulation. I have implemented the following integrator given Glenn Fiedler's tutorial: /// <summary> /// Represents physics state. /// </summary> public struct State { // Also used internally as derivative. // S: Position // D: Velocity. /// <summary> /// Gets or sets the Position. /// </summary> public Vector2 X; // S: Position // D: Acceleration. /// <summary> /// Gets or sets the Velocity. /// </summary> public Vector2 V; } /// <summary> /// Calculates the force given the specified state. /// </summary> /// <param name="state">The state.</param> /// <param name="t">The time.</param> /// <param name="acceleration">The value that should be updated with the acceleration.</param> public delegate void EulerIntegrator(ref State state, float t, ref Vector2 acceleration); /// <summary> /// Represents the RK4 Integrator. /// </summary> public static class RK4 { private const float OneSixth = 1.0f / 6.0f; private static void Evaluate(EulerIntegrator integrator, ref State initial, float t, float dt, ref State derivative, ref State output) { var state = new State(); // These are a premature optimization. I like premature optimization. // So let's not concentrate on that. state.X.X = initial.X.X + derivative.X.X * dt; state.X.Y = initial.X.Y + derivative.X.Y * dt; state.V.X = initial.V.X + derivative.V.X * dt; state.V.Y = initial.V.Y + derivative.V.Y * dt; output = new State(); output.X.X = state.V.X; output.X.Y = state.V.Y; integrator(ref state, t + dt, ref output.V); } /// <summary> /// Performs RK4 integration over the specified state. /// </summary> /// <param name="eulerIntegrator">The euler integrator.</param> /// <param name="state">The state.</param> /// <param name="t">The t.</param> /// <param name="dt">The dt.</param> public static void Integrate(EulerIntegrator eulerIntegrator, ref State state, float t, float dt) { var a = new State(); var b = new State(); var c = new State(); var d = new State(); Evaluate(eulerIntegrator, ref state, t, 0.0f, ref a, ref a); Evaluate(eulerIntegrator, ref state, t + dt * 0.5f, dt * 0.5f, ref a, ref b); Evaluate(eulerIntegrator, ref state, t + dt * 0.5f, dt * 0.5f, ref b, ref c); Evaluate(eulerIntegrator, ref state, t + dt, dt, ref c, ref d); a.X.X = OneSixth * (a.X.X + 2.0f * (b.X.X + c.X.X) + d.X.X); a.X.Y = OneSixth * (a.X.Y + 2.0f * (b.X.Y + c.X.Y) + d.X.Y); a.V.X = OneSixth * (a.V.X + 2.0f * (b.V.X + c.V.X) + d.V.X); a.V.Y = OneSixth * (a.V.Y + 2.0f * (b.V.Y + c.V.Y) + d.V.Y); state.X.X = state.X.X + a.X.X * dt; state.X.Y = state.X.Y + a.X.Y * dt; state.V.X = state.V.X + a.V.X * dt; state.V.Y = state.V.Y + a.V.Y * dt; } } After reading over the tutorial I noticed a few things that just seemed 'out' to me. Notably how the entire simulation revolves around t at 0 and state at 0 - considering that we are working out a curve over the duration it seems logical that RK4 wouldn't be able to handle this simple scenario. Never-the-less I forged on and wrote a very simple Euler integrator: static void Integrator(ref State state, float t, ref Vector2 acceleration) { if (state.X.Y > 100 && state.V.Y > 0) { // Bounce vertically. acceleration.Y = -state.V.Y * t; } else { acceleration.Y = 9.8f; } } I then ran the code against a simple fixed-time step loop and this is what I got: 0.05 0.20 0.44 0.78 1.23 1.76 ... 74.53 78.40 82.37 86.44 90.60 94.86 99.23 103.05 105.45 106.94 107.86 108.42 108.76 108.96 109.08 109.15 109.19 109.21 109.23 109.23 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 109.24 ... As I said, I was expecting it to break - however I am unsure of how to fix it. I am currently looking into keeping the previous state and time, and working from that - although at the same time I assume that will defeat the purpose of RK4. How would I get this simulation to print the expected results?

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• CUDA compare arrays

  - by user315511

  Hello. Trying to make an app that will compare 1-to-multiple bitmaps. there is one reference bitmap and multiple other bitmaps. Result from each compare should be new bitmap with diffs. Maybe comparing bitmaps rather as textures than arrays? My biggest problem is making kernel accept more than one input pointer, and how to compare the data.. extern "C" __global__ void compare(float *odata, float *idata, int width, int height) works and following does not (i call the function with enough params) extern "C" __global__ void compare(float *odata, float *idata, float *idata2, int width, int height)

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• Scalar-Valued Function in NHibernate

  - by Byron Sommardahl

  I have the following scalar function in MS SQL 2005: CREATE FUNCTION [dbo].[Distance] ( @lat1 float, @long1 float,@lat2 float, @long2 float ) RETURNS float AS BEGIN RETURN (3958*3.1415926*sqrt((@lat2-@lat1)*(@lat2-@lat1) + cos(@lat2/57.29578)*cos(@lat1/57.29578)*(@long2-@long1)*(@long2-@long1))/180); END I need to be able to call this function from my NHibernate queries. I read over this article, but I got bogged down in some details that I didn't understand right away. If you've used scalar functions with NHibernate, could you possibly give me an example of how your HBM file would look for a function like this?

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• First time shadow mapping problems

  - by user1294203

  I have implemented basic shadow mapping for the first time in OpenGL using shaders and I'm facing some problems. Below you can see an example of my rendered scene: The process of the shadow mapping I'm following is that I render the scene to the framebuffer using a View Matrix from the light point of view and the projection and model matrices used for normal rendering. In the second pass, I send the above MVP matrix from the light point of view to the vertex shader which transforms the position to light space. The fragment shader does the perspective divide and changes the position to texture coordinates. Here is my vertex shader, #version 150 core uniform mat4 ModelViewMatrix; uniform mat3 NormalMatrix; uniform mat4 MVPMatrix; uniform mat4 lightMVP; uniform float scale; in vec3 in_Position; in vec3 in_Normal; in vec2 in_TexCoord; smooth out vec3 pass_Normal; smooth out vec3 pass_Position; smooth out vec2 TexCoord; smooth out vec4 lightspace_Position; void main(void){ pass_Normal = NormalMatrix * in_Normal; pass_Position = (ModelViewMatrix * vec4(scale * in_Position, 1.0)).xyz; lightspace_Position = lightMVP * vec4(scale * in_Position, 1.0); TexCoord = in_TexCoord; gl_Position = MVPMatrix * vec4(scale * in_Position, 1.0); } And my fragment shader, #version 150 core struct Light{ vec3 direction; }; uniform Light light; uniform sampler2D inSampler; uniform sampler2D inShadowMap; smooth in vec3 pass_Normal; smooth in vec3 pass_Position; smooth in vec2 TexCoord; smooth in vec4 lightspace_Position; out vec4 out_Color; float CalcShadowFactor(vec4 lightspace_Position){ vec3 ProjectionCoords = lightspace_Position.xyz / lightspace_Position.w; vec2 UVCoords; UVCoords.x = 0.5 * ProjectionCoords.x + 0.5; UVCoords.y = 0.5 * ProjectionCoords.y + 0.5; float Depth = texture(inShadowMap, UVCoords).x; if(Depth < (ProjectionCoords.z + 0.001)) return 0.5; else return 1.0; } void main(void){ vec3 Normal = normalize(pass_Normal); vec3 light_Direction = -normalize(light.direction); vec3 camera_Direction = normalize(-pass_Position); vec3 half_vector = normalize(camera_Direction + light_Direction); float diffuse = max(0.2, dot(Normal, light_Direction)); vec3 temp_Color = diffuse * vec3(1.0); float specular = max( 0.0, dot( Normal, half_vector) ); float shadowFactor = CalcShadowFactor(lightspace_Position); if(diffuse != 0 && shadowFactor > 0.5){ float fspecular = pow(specular, 128.0); temp_Color += fspecular; } out_Color = vec4(shadowFactor * texture(inSampler, TexCoord).xyz * temp_Color, 1.0); } One of the problems is self shadowing as you can see in the picture, the crate has its own shadow cast on itself. What I have tried is enabling polygon offset (i.e. glEnable(POLYGON_OFFSET_FILL), glPolygonOffset(GLfloat, GLfloat) ) but it didn't change much. As you see in the fragment shader, I have put a static offset value of 0.001 but I have to change the value depending on the distance of the light to get more desirable effects , which not very handy. I also tried using front face culling when I render to the framebuffer, that didn't change much too. The other problem is that pixels outside the Light's view frustum get shaded. The only object that is supposed to be able to cast shadows is the crate. I guess I should pick more appropriate projection and view matrices, but I'm not sure how to do that. What are some common practices, should I pick an orthographic projection? From googling around a bit, I understand that these issues are not that trivial. Does anyone have any easy to implement solutions to these problems. Could you give me some additional tips? Please ask me if you need more information on my code. Here is a comparison with and without shadow mapping of a close-up of the crate. The self-shadowing is more visible.

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• How to label a cuboid?

  - by usha

  Hi this is how my 3dcuboid looks, I have attached the complete code. I want to label this cuboid using different names across sides, how is this possible using opengl on android? public class MyGLRenderer implements Renderer { Context context; Cuboid rect; private float mCubeRotation; // private static float angleCube = 0; // Rotational angle in degree for cube (NEW) // private static float speedCube = -1.5f; // Rotational speed for cube (NEW) public MyGLRenderer(Context context) { rect = new Cuboid(); this.context = context; } public void onDrawFrame(GL10 gl) { // TODO Auto-generated method stub gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT); gl.glLoadIdentity(); // Reset the model-view matrix gl.glTranslatef(0.2f, 0.0f, -8.0f); // Translate right and into the screen gl.glScalef(0.8f, 0.8f, 0.8f); // Scale down (NEW) gl.glRotatef(mCubeRotation, 1.0f, 1.0f, 1.0f); // gl.glRotatef(angleCube, 1.0f, 1.0f, 1.0f); // rotate about the axis (1,1,1) (NEW) rect.draw(gl); mCubeRotation -= 0.15f; //angleCube += speedCube; } public void onSurfaceChanged(GL10 gl, int width, int height) { // TODO Auto-generated method stub if (height == 0) height = 1; // To prevent divide by zero float aspect = (float)width / height; // Set the viewport (display area) to cover the entire window gl.glViewport(0, 0, width, height); // Setup perspective projection, with aspect ratio matches viewport gl.glMatrixMode(GL10.GL_PROJECTION); // Select projection matrix gl.glLoadIdentity(); // Reset projection matrix // Use perspective projection GLU.gluPerspective(gl, 45, aspect, 0.1f, 100.f); gl.glMatrixMode(GL10.GL_MODELVIEW); // Select model-view matrix gl.glLoadIdentity(); // Reset } public void onSurfaceCreated(GL10 gl, EGLConfig config) { // TODO Auto-generated method stub gl.glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set color's clear-value to black gl.glClearDepthf(1.0f); // Set depth's clear-value to farthest gl.glEnable(GL10.GL_DEPTH_TEST); // Enables depth-buffer for hidden surface removal gl.glDepthFunc(GL10.GL_LEQUAL); // The type of depth testing to do gl.glHint(GL10.GL_PERSPECTIVE_CORRECTION_HINT, GL10.GL_NICEST); // nice perspective view gl.glShadeModel(GL10.GL_SMOOTH); // Enable smooth shading of color gl.glDisable(GL10.GL_DITHER); // Disable dithering for better performance }} public class Cuboid{ private FloatBuffer mVertexBuffer; private FloatBuffer mColorBuffer; private ByteBuffer mIndexBuffer; private float vertices[] = { //width,height,depth -2.5f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -2.5f, 1.0f, -1.0f, -2.5f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -2.5f, 1.0f, 1.0f }; private float colors[] = { // R,G,B,A COLOR 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 1.0f, 0.5f, 0.0f, 1.0f, 1.0f, 0.5f, 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 1.0f, 0.0f, 1.0f, 1.0f }; private byte indices[] = { // VERTEX 0,1,2,3,4,5,6,7 REPRESENTATION FOR FACES 0, 4, 5, 0, 5, 1, 1, 5, 6, 1, 6, 2, 2, 6, 7, 2, 7, 3, 3, 7, 4, 3, 4, 0, 4, 7, 6, 4, 6, 5, 3, 0, 1, 3, 1, 2 }; public Cuboid() { ByteBuffer byteBuf = ByteBuffer.allocateDirect(vertices.length * 4); byteBuf.order(ByteOrder.nativeOrder()); mVertexBuffer = byteBuf.asFloatBuffer(); mVertexBuffer.put(vertices); mVertexBuffer.position(0); byteBuf = ByteBuffer.allocateDirect(colors.length * 4); byteBuf.order(ByteOrder.nativeOrder()); mColorBuffer = byteBuf.asFloatBuffer(); mColorBuffer.put(colors); mColorBuffer.position(0); mIndexBuffer = ByteBuffer.allocateDirect(indices.length); mIndexBuffer.put(indices); mIndexBuffer.position(0); } public void draw(GL10 gl) { gl.glFrontFace(GL10.GL_CW); gl.glVertexPointer(3, GL10.GL_FLOAT, 0, mVertexBuffer); gl.glColorPointer(4, GL10.GL_FLOAT, 0, mColorBuffer); gl.glEnableClientState(GL10.GL_VERTEX_ARRAY); gl.glEnableClientState(GL10.GL_COLOR_ARRAY); gl.glDrawElements(GL10.GL_TRIANGLES, 36, GL10.GL_UNSIGNED_BYTE, mIndexBuffer); gl.glDisableClientState(GL10.GL_VERTEX_ARRAY); gl.glDisableClientState(GL10.GL_COLOR_ARRAY); } } public class Draw3drect extends Activity { private GLSurfaceView glView; // Use GLSurfaceView // Call back when the activity is started, to initialize the view @Override protected void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); glView = new GLSurfaceView(this); // Allocate a GLSurfaceView glView.setRenderer(new MyGLRenderer(this)); // Use a custom renderer this.setContentView(glView); // This activity sets to GLSurfaceView } // Call back when the activity is going into the background @Override protected void onPause() { super.onPause(); glView.onPause(); } // Call back after onPause() @Override protected void onResume() { super.onResume(); glView.onResume(); } }

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• Repeated Squaring - Matrix Multiplication using NEWMAT

  - by Dinakar Kulkarni

  I'm trying to use the repeated squaring algorithm (using recursion) to perform matrix exponentiation. I've included header files from the NEWMAT library instead of using arrays. The original matrix has elements in the range (-5,5), all numbers being of type float. # include "C:\User\newmat10\newmat.h" # include "C:\User\newmat10\newmatio.h" # include "C:\User\newmat10\newmatap.h" # include <iostream> # include <time.h> # include <ctime> # include <cstdlib> # include <iomanip> using namespace std; Matrix repeated_squaring(Matrix A, int exponent, int n) //Recursive function { A(n,n); IdentityMatrix I(n); if (exponent == 0) //Matrix raised to zero returns an Identity Matrix return I; else { if ( exponent%2 == 1 ) // if exponent is odd return (A * repeated_squaring (A*A, (exponent-1)/2, n)); else //if exponent is even return (A * repeated_squaring( A*A, exponent/2, n)); } } Matrix direct_squaring(Matrix B, int k, int no) //Brute Force Multiplication { B(no,no); Matrix C = B; for (int i = 1; i <= k; i++) C = B*C; return C; } //----Creating a matrix with elements b/w (-5,5)---- float unifRandom() { int a = -5; int b = 5; float temp = (float)((b-a)*( rand()/RAND_MAX) + a); return temp; } Matrix initialize_mat(Matrix H, int ord) { H(ord,ord); for (int y = 1; y <= ord; y++) for(int z = 1; z<= ord; z++) H(y,z) = unifRandom(); return(H); } //--------------------------------------------------- void main() { int exponent, dimension; cout<<"Insert exponent:"<<endl; cin>>exponent; cout<< "Insert dimension:"<<endl; cin>>dimension; cout<<"The number of rows/columns in the square matrix is: "<<dimension<<endl; cout<<"The exponent is: "<<exponent<<endl; Matrix A(dimension,dimension),B(dimension,dimension); Matrix C(dimension,dimension),D(dimension,dimension); B= initialize_mat(A,dimension); cout<<"Initial Matrix: "<<endl; cout<<setw(5)<<setprecision(2)<<B<<endl; //----------------------------------------------------------------------------- cout<<"Repeated Squaring Result: "<<endl; clock_t time_before1 = clock(); C = repeated_squaring (B, exponent , dimension); cout<< setw(5) <<setprecision(2) <<C; clock_t time_after1 = clock(); float diff1 = ((float) time_after1 - (float) time_before1); cout << "It took " << diff1/CLOCKS_PER_SEC << " seconds to complete" << endl<<endl; //--------------------------------------------------------------------------------- cout<<"Direct Squaring Result:"<<endl; clock_t time_before2 = clock(); D = direct_squaring (B, exponent , dimension); cout<<setw(5)<<setprecision(2)<<D; clock_t time_after2 = clock(); float diff2 = ((float) time_after2 - (float) time_before2); cout << "It took " << diff2/CLOCKS_PER_SEC << " seconds to complete" << endl<<endl; } I face the following problems: The random number generator returns only "-5" as each element in the output. The Matrix multiplication yield different results with brute force multiplication and using the repeated squaring algorithm. I'm timing the execution time of my code to compare the times taken by brute force multiplication and by repeated squaring. Could someone please find out what's wrong with the recursion and with the matrix initialization? NOTE: While compiling this program, make sure you've imported the NEWMAT library. Thanks in advance!

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• Which of these algorithms is best for my goal?

  - by JonathonG

  I have created a program that restricts the mouse to a certain region based on a black/white bitmap. The program is 100% functional as-is, but uses an inaccurate, albeit fast, algorithm for repositioning the mouse when it strays outside the area. Currently, when the mouse moves outside the area, basically what happens is this: A line is drawn between a pre-defined static point inside the region and the mouse's new position. The point where that line intersects the edge of the allowed area is found. The mouse is moved to that point. This works, but only works perfectly for a perfect circle with the pre-defined point set in the exact center. Unfortunately, this will never be the case. The application will be used with a variety of rectangles and irregular, amorphous shapes. On such shapes, the point where the line drawn intersects the edge will usually not be the closest point on the shape to the mouse. I need to create a new algorithm that finds the closest point to the mouse's new position on the edge of the allowed area. I have several ideas about this, but I am not sure of their validity, in that they may have far too much overhead. While I am not asking for code, it might help to know that I am using Objective C / Cocoa, developing for OS X, as I feel the language being used might affect the efficiency of potential methods. My ideas are: Using a bit of trigonometry to project lines would work, but that would require some kind of intense algorithm to test every point on every line until it found the edge of the region... That seems too resource intensive since there could be something like 200 lines that would have each have to have as many as 200 pixels checked for black/white.... Using something like an A* pathing algorithm to find the shortest path to a black pixel; however, A* seems resource intensive, even though I could probably restrict it to only checking roughly in one direction. It also seems like it will take more time and effort than I have available to spend on this small portion of the much larger project I am working on, correct me if I am wrong and it would not be a significant amount of code (100 lines or around there). Mapping the border of the region before the application begins running the event tap loop. I think I could accomplish this by using my current line-based algorithm to find an edge point and then initiating an algorithm that checks all 8 pixels around that pixel, finds the next border pixel in one direction, and continues to do this until it comes back to the starting pixel. I could then store that data in an array to be used for the entire duration of the program, and have the mouse re-positioning method check the array for the closest pixel on the border to the mouse target position. That last method would presumably execute it's initial border mapping fairly quickly. (It would only have to map between 2,000 and 8,000 pixels, which means 8,000 to 64,000 checked, and I could even permanently store the data to make launching faster.) However, I am uncertain as to how much overhead it would take to scan through that array for the shortest distance for every single mouse move event... I suppose there could be a shortcut to restrict the number of elements in the array that will be checked to a variable number starting with the intersecting point on the line (from my original algorithm), and raise/lower that number to experiment with the overhead/accuracy tradeoff. Please let me know if I am over thinking this and there is an easier way that will work just fine, or which of these methods would be able to execute something like 30 times per second to keep mouse movement smooth, or if you have a better/faster method. I've posted relevant parts of my code below for reference, and included an example of what the area might look like. (I check for color value against a loaded bitmap that is black/white.) // // This part of my code runs every single time the mouse moves. // CGPoint point = CGEventGetLocation(event); float tX = point.x; float tY = point.y; if( is_in_area(tX,tY, mouse_mask)){ // target is inside O.K. area, do nothing }else{ CGPoint target; //point inside restricted region: float iX = 600; // inside x float iY = 500; // inside y // delta to midpoint between iX,iY and tX,tY float dX; float dY; float accuracy = .5; //accuracy to loop until reached do { dX = (tX-iX)/2; dY = (tY-iY)/2; if(is_in_area((tX-dX),(tY-dY),mouse_mask)){ iX += dX; iY += dY; } else { tX -= dX; tY -= dY; } } while (abs(dX)>accuracy || abs(dY)>accuracy); target = CGPointMake(roundf(tX), roundf(tY)); CGDisplayMoveCursorToPoint(CGMainDisplayID(),target); } Here is "is_in_area(int x, int y)" : bool is_in_area(NSInteger x, NSInteger y, NSBitmapImageRep *mouse_mask){ NSAutoreleasePool * pool = [[NSAutoreleasePool alloc] init]; NSUInteger pixel[4]; [mouse_mask getPixel:pixel atX:x y:y]; if(pixel[0]!= 0){ [pool release]; return false; } [pool release]; return true; }

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• MinGW and "declaration does not declare anything"

  - by Bob Somers

  I'm working on converting a Linux project of mine to compile on Windows using MinGW. It compiles and runs just fine on Linux, but when I attempt to compile it with MinGW it bombs out with the following error message: camera.h:11: error: declaration does not declare anything camera.h:12: error: declaration does not declare anything I'm kind of baffled why this is happening, because I'm using the same version of g++ (4.4) on both Linux and Windows (via MinGW). The contents of camera.h is absurdly simple. Here's the code. It's choking on lines 11 and 12 where float near; and float far; are defined. #include "Vector.h" #ifndef _CAMERA_H_ #define _CAMERA_H_ class Camera{ public: Vector eye; Vector lookAt; float fov; float near; float far; }; #endif Thanks for your help.

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• Android v1.5 w/ browser data storage

  - by Sirber

  I'm trying to build an offline web application which can sync online if the network is available. I tryed jQuery jStore but the test page stop at "testing..." whitout result, then I tryed Google Gears which is supposed to be working on the phone but it gears is not found. if (window.google && google.gears) { google.gears.factory.getPermission(); // Database var db = google.gears.factory.create('beta.database'); db.open('cominar-compteurs'); db.execute('create table if not exists Lectures' + ' (ID_COMPTEUR int, DATE_HEURE timestamp, kWh float, Wmax float, VAmax float, Wcum float, VAcum float);'); } else { alert('Google Gears non trouvé.'); } the code does work on Google Chrome v5.

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• MinGW and "delcaration does not declare anything"

  - by Bob Somers

  I'm working on converting a Linux project of mine to compile on Windows using MinGW. It compiles and runs just fine on Linux, but when I attempt to compile it with MinGW it bombs out with the following error message: camera.h:11: error: declaration does not declare anything camera.h:12: error: declaration does not declare anything I'm kind of baffled why this is happening, because I'm using the same version of g++ (4.4) on both Linux and Windows (via MinGW). The contents of camera.h is absurdly simple. Here's the code. It's choking on lines 11 and 12 where float near; and float far; are defined. #include "Vector.h" #ifndef _CAMERA_H_ #define _CAMERA_H_ class Camera{ public: Vector eye; Vector lookAt; float fov; float near; float far; }; #endif Thanks for your help.

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• how to label a cuboid using open gl?

  - by usha

  hi this is how my 3dcuboid looks ,i have attached complete code , i want to label this cuboid using different name across sides how is it possible using opengl in android...plz help me out public class MyGLRenderer implements Renderer { Context context; Cuboid rect; private float mCubeRotation; // private static float angleCube = 0; // Rotational angle in degree for cube (NEW) // private static float speedCube = -1.5f; // Rotational speed for cube (NEW) public MyGLRenderer(Context context) { rect = new Cuboid(); this.context = context; } public void onDrawFrame(GL10 gl) { // TODO Auto-generated method stub gl.glClear(GL10.GL_COLOR_BUFFER_BIT | GL10.GL_DEPTH_BUFFER_BIT); gl.glLoadIdentity(); // Reset the model-view matrix gl.glTranslatef(0.2f, 0.0f, -8.0f); // Translate right and into the screen gl.glScalef(0.8f, 0.8f, 0.8f); // Scale down (NEW) gl.glRotatef(mCubeRotation, 1.0f, 1.0f, 1.0f); // gl.glRotatef(angleCube, 1.0f, 1.0f, 1.0f); // rotate about the axis (1,1,1) (NEW) rect.draw(gl); mCubeRotation -= 0.15f; //angleCube += speedCube; } public void onSurfaceChanged(GL10 gl, int width, int height) { // TODO Auto-generated method stub if (height == 0) height = 1; // To prevent divide by zero float aspect = (float)width / height; // Set the viewport (display area) to cover the entire window gl.glViewport(0, 0, width, height); // Setup perspective projection, with aspect ratio matches viewport gl.glMatrixMode(GL10.GL_PROJECTION); // Select projection matrix gl.glLoadIdentity(); // Reset projection matrix // Use perspective projection GLU.gluPerspective(gl, 45, aspect, 0.1f, 100.f); gl.glMatrixMode(GL10.GL_MODELVIEW); // Select model-view matrix gl.glLoadIdentity(); // Reset } public void onSurfaceCreated(GL10 gl, EGLConfig config) { // TODO Auto-generated method stub gl.glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set color's clear-value to black gl.glClearDepthf(1.0f); // Set depth's clear-value to farthest gl.glEnable(GL10.GL_DEPTH_TEST); // Enables depth-buffer for hidden surface removal gl.glDepthFunc(GL10.GL_LEQUAL); // The type of depth testing to do gl.glHint(GL10.GL_PERSPECTIVE_CORRECTION_HINT, GL10.GL_NICEST); // nice perspective view gl.glShadeModel(GL10.GL_SMOOTH); // Enable smooth shading of color gl.glDisable(GL10.GL_DITHER); // Disable dithering for better performance }} public class Cuboid{ private FloatBuffer mVertexBuffer; private FloatBuffer mColorBuffer; private ByteBuffer mIndexBuffer; private float vertices[] = { //width,height,depth -2.5f, -1.0f, -1.0f, 1.0f, -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -2.5f, 1.0f, -1.0f, -2.5f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -2.5f, 1.0f, 1.0f }; private float colors[] = { // R,G,B,A COLOR 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 0.0f, 1.0f, 1.0f, 0.5f, 0.0f, 1.0f, 1.0f, 0.5f, 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 1.0f, 1.0f, 1.0f, 0.0f, 1.0f, 1.0f }; private byte indices[] = { // VERTEX 0,1,2,3,4,5,6,7 REPRESENTATION FOR FACES 0, 4, 5, 0, 5, 1, 1, 5, 6, 1, 6, 2, 2, 6, 7, 2, 7, 3, 3, 7, 4, 3, 4, 0, 4, 7, 6, 4, 6, 5, 3, 0, 1, 3, 1, 2 }; public Cuboid() { ByteBuffer byteBuf = ByteBuffer.allocateDirect(vertices.length * 4); byteBuf.order(ByteOrder.nativeOrder()); mVertexBuffer = byteBuf.asFloatBuffer(); mVertexBuffer.put(vertices); mVertexBuffer.position(0); byteBuf = ByteBuffer.allocateDirect(colors.length * 4); byteBuf.order(ByteOrder.nativeOrder()); mColorBuffer = byteBuf.asFloatBuffer(); mColorBuffer.put(colors); mColorBuffer.position(0); mIndexBuffer = ByteBuffer.allocateDirect(indices.length); mIndexBuffer.put(indices); mIndexBuffer.position(0); } public void draw(GL10 gl) { gl.glFrontFace(GL10.GL_CW); gl.glVertexPointer(3, GL10.GL_FLOAT, 0, mVertexBuffer); gl.glColorPointer(4, GL10.GL_FLOAT, 0, mColorBuffer); gl.glEnableClientState(GL10.GL_VERTEX_ARRAY); gl.glEnableClientState(GL10.GL_COLOR_ARRAY); gl.glDrawElements(GL10.GL_TRIANGLES, 36, GL10.GL_UNSIGNED_BYTE, mIndexBuffer); gl.glDisableClientState(GL10.GL_VERTEX_ARRAY); gl.glDisableClientState(GL10.GL_COLOR_ARRAY); } } public class Draw3drect extends Activity { private GLSurfaceView glView; // Use GLSurfaceView // Call back when the activity is started, to initialize the view @Override protected void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); glView = new GLSurfaceView(this); // Allocate a GLSurfaceView glView.setRenderer(new MyGLRenderer(this)); // Use a custom renderer this.setContentView(glView); // This activity sets to GLSurfaceView } // Call back when the activity is going into the background @Override protected void onPause() { super.onPause(); glView.onPause(); } // Call back after onPause() @Override protected void onResume() { super.onResume(); glView.onResume(); } }

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• Need help in translating code from C to Java.

  - by Vuntic

  From this article. Here's the code: float InvSqrt(float x){ // line 0 float xhalf = 0.5f * x; int i = *(int*)&x; // store floating-point bits in integer i = 0x5f3759d5 - (i >> 1); // initial guess for Newton's method x = *(float*)&i; // convert new bits into float x = x*(1.5f - xhalf*x*x); // One round of Newton's method return x; } ...I can't even tell if that's C or C++. [okay apparently it's C, thanks] Could someone translate it to Java for me, please? It's (only, I hope) lines 2 and 4 that are confusing me.

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• Need help in translating code from C or C++ to Java.

  - by Vuntic

  From this article. Here's the code: float InvSqrt(float x){ // line 0 float xhalf = 0.5f * x; int i = *(int*)&x; // store floating-point bits in integer i = 0x5f3759d5 - (i >> 1); // initial guess for Newton's method x = *(float*)&i; // convert new bits into float x = x*(1.5f - xhalf*x*x); // One round of Newton's method return x; } ...I can't even tell if that's C or C++. Could someone translate it to Java for me, please? It's (only, I hope) lines 2 and 4 that are confusing me. I'll edit out the confusion about C/C++ from the tags once somebody tells me which it is.

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• xcode 4 creating a 2d grid (range and domain)

  - by user1706978

  I'm learning how to program c and i'm trying to make a program the finds the range (using an equation with x as the domain) of a 2d grid...ive already attempted it, but it's giving me all these errors on Xcode, any help?(As you can see, I'm quite stuck!) #include <stdio.h> #include <stdlib.h> float domain; float domain = 2.0; float domainsol(float x ) { domain = x; float func = 1.25 * x + 5.0; return func; } int main(int argc, const char * argv[]) { }

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• Initializing and drawing a mesh using OpenTK

  - by Boreal

  I'm implementing a "Mesh" class to use in my OpenTK game. You pass in a vertex array and an index array, and then you can call Mesh.Draw() to draw it using a shader. I've heard VBO's and VAO's are the way to go for this approach, but nowhere have I found a guide that shows how to get Data Video Memory Shader. Can someone give me a quick rundown of how this works? EDIT: So far, I have this: struct Vertex { public Vector3 position; public Vector3 normal; public Vector3 color; public static int memSize = 9 * sizeof(float); public static byte[] memOffset = { 0, 3 * sizeof(float), 6 * sizeof(float) }; } class Mesh { private uint vbo; private uint ibo; // stores the numbers of vertices and indices private int numVertices; private int numIndices; public Mesh(int numVertices, Vertex[] vertices, int numIndices, ushort[] indices) { // set numbers this.numVertices = numVertices; this.numIndices = numIndices; // generate buffers GL.GenBuffers(1, out vbo); GL.GenBuffers(1, out ibo); GL.BindBuffer(BufferTarget.ArrayBuffer, vbo); GL.BindBuffer(BufferTarget.ElementArrayBuffer, ibo); // send data to the buffers GL.BufferData(BufferTarget.ArrayBuffer, new IntPtr(Vertex.memSize * numVertices), vertices, BufferUsageHint.StaticDraw); GL.BufferData(BufferTarget.ElementArrayBuffer, new IntPtr(sizeof(ushort) * numIndices), indices, BufferUsageHint.StaticDraw); } public void Render() { // bind buffers GL.BindBuffer(BufferTarget.ArrayBuffer, vbo); GL.BindBuffer(BufferTarget.ElementArrayBuffer, ibo); // define offsets GL.VertexPointer(3, VertexPointerType.Float, Vertex.memSize, new IntPtr(Vertex.memOffset[0])); GL.NormalPointer(NormalPointerType.Float, Vertex.memSize, new IntPtr(Vertex.memOffset[1])); GL.ColorPointer(3, ColorPointerType.Float, Vertex.memSize, new IntPtr(Vertex.memOffset[2])); // draw GL.DrawElements(BeginMode.Triangles, numIndices, DrawElementsType.UnsignedInt, (IntPtr)0); } } class Application : GameWindow { Mesh triangle; protected override void OnLoad(EventArgs e) { base.OnLoad(e); GL.ClearColor(0.1f, 0.2f, 0.5f, 0.0f); GL.Enable(EnableCap.DepthTest); GL.Enable(EnableCap.VertexArray); GL.Enable(EnableCap.NormalArray); GL.Enable(EnableCap.ColorArray); Vertex v0 = new Vertex(); v0.position = new Vector3(-1.0f, -1.0f, 4.0f); v0.normal = new Vector3(0.0f, 0.0f, -1.0f); v0.color = new Vector3(1.0f, 1.0f, 0.0f); Vertex v1 = new Vertex(); v1.position = new Vector3(1.0f, -1.0f, 4.0f); v1.normal = new Vector3(0.0f, 0.0f, -1.0f); v1.color = new Vector3(1.0f, 0.0f, 0.0f); Vertex v2 = new Vertex(); v2.position = new Vector3(0.0f, 1.0f, 4.0f); v2.normal = new Vector3(0.0f, 0.0f, -1.0f); v2.color = new Vector3(0.2f, 0.9f, 1.0f); Vertex[] va = { v0, v1, v2 }; ushort[] ia = { 0, 1, 2 }; triangle = new Mesh(3, va, 3, ia); } protected override void OnRenderFrame(FrameEventArgs e) { base.OnRenderFrame(e); GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit); Matrix4 modelview = Matrix4.LookAt(Vector3.Zero, Vector3.UnitZ, Vector3.UnitY); GL.MatrixMode(MatrixMode.Modelview); GL.LoadMatrix(ref modelview); triangle.Render(); SwapBuffers(); } } It doesn't draw anything.

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• Ambient occlusion shader just shows models as all white

  - by dvds414

  Okay so I have this shader for ambient occlusion. It loads to world correctly, but it just shows all the models as being white. I do not know why. I am just running the shader while the model is rendering, is that correct? or do I need to make a render target or something? If so then how? I'm using C++. Here is my shader: float sampleRadius; float distanceScale; float4x4 xProjection; float4x4 xView; float4x4 xWorld; float3 cornerFustrum; struct VS_OUTPUT { float4 pos : POSITION; float2 TexCoord : TEXCOORD0; float3 viewDirection : TEXCOORD1; }; VS_OUTPUT VertexShaderFunction( float4 Position : POSITION, float2 TexCoord : TEXCOORD0) { VS_OUTPUT Out = (VS_OUTPUT)0; float4 WorldPosition = mul(Position, xWorld); float4 ViewPosition = mul(WorldPosition, xView); Out.pos = mul(ViewPosition, xProjection); Position.xy = sign(Position.xy); Out.TexCoord = (float2(Position.x, -Position.y) + float2( 1.0f, 1.0f ) ) * 0.5f; float3 corner = float3(-cornerFustrum.x * Position.x, cornerFustrum.y * Position.y, cornerFustrum.z); Out.viewDirection = corner; return Out; } texture depthTexture; texture randomTexture; sampler2D depthSampler = sampler_state { Texture = <depthTexture>; ADDRESSU = CLAMP; ADDRESSV = CLAMP; MAGFILTER = LINEAR; MINFILTER = LINEAR; }; sampler2D RandNormal = sampler_state { Texture = <randomTexture>; ADDRESSU = WRAP; ADDRESSV = WRAP; MAGFILTER = LINEAR; MINFILTER = LINEAR; }; float4 PixelShaderFunction(VS_OUTPUT IN) : COLOR0 { float4 samples[16] = { float4(0.355512, -0.709318, -0.102371, 0.0 ), float4(0.534186, 0.71511, -0.115167, 0.0 ), float4(-0.87866, 0.157139, -0.115167, 0.0 ), float4(0.140679, -0.475516, -0.0639818, 0.0 ), float4(-0.0796121, 0.158842, -0.677075, 0.0 ), float4(-0.0759516, -0.101676, -0.483625, 0.0 ), float4(0.12493, -0.0223423, -0.483625, 0.0 ), float4(-0.0720074, 0.243395, -0.967251, 0.0 ), float4(-0.207641, 0.414286, 0.187755, 0.0 ), float4(-0.277332, -0.371262, 0.187755, 0.0 ), float4(0.63864, -0.114214, 0.262857, 0.0 ), float4(-0.184051, 0.622119, 0.262857, 0.0 ), float4(0.110007, -0.219486, 0.435574, 0.0 ), float4(0.235085, 0.314707, 0.696918, 0.0 ), float4(-0.290012, 0.0518654, 0.522688, 0.0 ), float4(0.0975089, -0.329594, 0.609803, 0.0 ) }; IN.TexCoord.x += 1.0/1600.0; IN.TexCoord.y += 1.0/1200.0; normalize (IN.viewDirection); float depth = tex2D(depthSampler, IN.TexCoord).a; float3 se = depth * IN.viewDirection; float3 randNormal = tex2D( RandNormal, IN.TexCoord * 200.0 ).rgb; float3 normal = tex2D(depthSampler, IN.TexCoord).rgb; float finalColor = 0.0f; for (int i = 0; i < 16; i++) { float3 ray = reflect(samples[i].xyz,randNormal) * sampleRadius; //if (dot(ray, normal) < 0) // ray += normal * sampleRadius; float4 sample = float4(se + ray, 1.0f); float4 ss = mul(sample, xProjection); float2 sampleTexCoord = 0.5f * ss.xy/ss.w + float2(0.5f, 0.5f); sampleTexCoord.x += 1.0/1600.0; sampleTexCoord.y += 1.0/1200.0; float sampleDepth = tex2D(depthSampler, sampleTexCoord).a; if (sampleDepth == 1.0) { finalColor ++; } else { float occlusion = distanceScale* max(sampleDepth - depth, 0.0f); finalColor += 1.0f / (1.0f + occlusion * occlusion * 0.1); } } return float4(finalColor/16, finalColor/16, finalColor/16, 1.0f); } technique SSAO { pass P0 { VertexShader = compile vs_3_0 VertexShaderFunction(); PixelShader = compile ps_3_0 PixelShaderFunction(); } }

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• From NaN to Infinity...and Beyond!

  - by Tony Davis

  It is hard to believe that it was once possible to corrupt a SQL Server Database by storing perfectly normal data values into a table; but it is true. In SQL Server 2000 and before, one could inadvertently load invalid data values into certain data types via RPC calls or bulk insert methods rather than DML. In the particular case of the FLOAT data type, this meant that common 'special values' for this type, namely NaN (not-a-number) and +/- infinity, could be quite happily plugged into the database from an application and stored as 'out-of-range' values. This was like a time-bomb. When one then tried to query this data; the values were unsupported and so data pages containing them were flagged as being corrupt. Any query that needed to read a column containing the special value could fail or return unpredictable results. Microsoft even had to issue a hotfix to deal with failures in the automatic recovery process, caused by the presence of these NaN values, which rendered the whole database inaccessible! This problem is history for those of us on more current versions of SQL Server, but its ghost still haunts us. Recently, for example, a developer on Red Gate’s SQL Response team reported a strange problem when attempting to load historical monitoring data into a SQL Server 2005 database via the C# ADO.NET provider. The ratios used in some of their reporting calculations occasionally threw out NaN or infinity values, and the subsequent attempts to load these values resulted in a nasty error. It turns out to be a different manifestation of the same problem. SQL Server 2005 still does not fully support the IEEE 754 standard for floating point numbers, in that the FLOAT data type still cannot handle NaN or infinity values. Instead, they just added validation checks that prevent the 'invalid' values from being loaded in the first place. For people migrating from SQL Server 2000 databases that contained out-of-range FLOAT (or DATETIME etc.) data, to SQL Server 2005, Microsoft have added to the latter's version of the DBCC CHECKDB (or CHECKTABLE) command a DATA_PURITY clause. When enabled, this will seek out the corrupt data, but won’t fix it. You have to do this yourself in what can often be a slow, painful manual process. Our development team, after a quizzical shrug of the shoulders, simply decided to represent NaN and infinity values as NULL, and move on, accepting the minor inconvenience of not being able to tell them apart. However, what of scientific, engineering and other applications that really would like the luxury of being able to both store and access these perfectly-reasonable floating point data values? The sticking point seems to be the stipulation in the IEEE 754 standard that, when NaN is compared to any other value including itself, the answer is "unequal" (i.e. FALSE). This is clearly different from normal number comparisons and has repercussions for such things as indexing operations. Even so, this hardly applies to infinity values, which are single definite values. In fact, there is some encouraging talk in the Connect note on this issue that they might be supported 'in the SQL Server 2008 timeframe'. If didn't happen; SQL 2008 doesn't support NaN or infinity values, though one could be forgiven for thinking otherwise, based on the MSDN documentation for the FLOAT type, which states that "The behavior of float and real follows the IEEE 754 specification on approximate numeric data types". However, the truth is revealed in the XPath documentation, which states that "…float (53) is not exactly IEEE 754. For example, neither NaN (Not-a-Number) nor infinity is used…". Is it really so hard to fix this problem the right way, and properly support in SQL Server the IEEE 754 standard for the floating point data type, NaNs, infinities and all? Oracle seems to have managed it quite nicely with its BINARY_FLOAT and BINARY_DOUBLE types, so it is technically possible. We have an enterprise-class database that is marketed as being part of an 'integrated' Windows platform. Absurdly, we have .NET and XPath libraries that fully support the standard for floating point numbers, and we can't even properly store these values, let alone query them, in the SQL Server database! Cheers, Tony.

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• Improving performance of a particle system (OpenGL ES)

  - by Jason

  I'm in the process of implementing a simple particle system for a 2D mobile game (using OpenGL ES 2.0). It's working, but it's pretty slow. I start getting frame rate battering after about 400 particles, which I think is pretty low. Here's a summary of my approach: I start with point sprites (GL_POINTS) rendered in a batch just using a native float buffer (I'm in Java-land on Android, so that translates as a java.nio.FloatBuffer). On GL context init, the following are set: GLES20.glViewport(0, 0, width, height); GLES20.glClearColor(0.0f, 0.0f, 0.0f, 0.0f); GLES20.glEnable(GLES20.GL_CULL_FACE); GLES20.glDisable(GLES20.GL_DEPTH_TEST); Each draw frame sets the following: GLES20.glEnable(GLES20.GL_BLEND); GLES20.glBlendFunc(GLES20.GL_ONE, GLES20.GL_ONE_MINUS_SRC_ALPHA); And I bind a single texture: GLES20.glActiveTexture(GLES20.GL_TEXTURE0); GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, textureHandle); GLES20.glUniform1i(mUniformTextureHandle, 0); Which is just a simple circle with some blur (and hence some transparency) http://cl.ly/image/0K2V2p2L1H2x Then there are a bunch of glVertexAttribPointer calls: mBuffer.position(position); mGlEs20.glVertexAttribPointer(mAttributeRGBHandle, valsPerRGB, GLES20.GL_FLOAT, false, stride, mBuffer); ...4 more of these Then I'm drawing: GLES20.glUniformMatrix4fv(mUniformProjectionMatrixHandle, 1, false, Camera.mProjectionMatrix, 0); GLES20.glDrawArrays(GLES20.GL_POINTS, 0, drawCalls); GLES20.glBindTexture(GLES20.GL_TEXTURE_2D, 0); My vertex shader does have some computation in it, but given that they're point sprites (with only 2 coordinate values) I'm not sure this is the problem: #ifdef GL_ES // Set the default precision to low. precision lowp float; #endif uniform mat4 u_ProjectionMatrix; attribute vec4 a_Position; attribute float a_PointSize; attribute vec3 a_RGB; attribute float a_Alpha; attribute float a_Burn; varying vec4 v_Color; void main() { vec3 v_FGC = a_RGB * a_Alpha; v_Color = vec4(v_FGC.x, v_FGC.y, v_FGC.z, a_Alpha * (1.0 - a_Burn)); gl_PointSize = a_PointSize; gl_Position = u_ProjectionMatrix * a_Position; } My fragment shader couldn't really be simpler: #ifdef GL_ES // Set the default precision to low. precision lowp float; #endif uniform sampler2D u_Texture; varying vec4 v_Color; void main() { gl_FragColor = texture2D(u_Texture, gl_PointCoord) * v_Color; } That's about it. I had read that transparent pixels in point sprites can cause issues, but surely not at only 400 points? I'm running on a fairly new device (12 month old Galaxy Nexus). My question is less about my approach (although I'm open to suggestion) but more about whether there are any specific OpenGL "no no's" that have leaked into my code. I'm sure there's GL master out there facepalming right now... I'd love to hear any critique.

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• Sprite animation in openGL - Some frames are being skipped

  - by Sid

  Earlier, I was facing problems on implementing sprite animation in openGL ES. Now its being sorted up. But the problem that i am facing now is that some of my frames are being skipped when a bullet(a circle) strikes on it. What I need : A sprite animation should stop at the last frame without skipping any frame. What I did : Collision Detection function and working properly. PS : Everything is working fine but i want to implement the animation in OPENGL ONLY. Canvas won't work in my case. ------------------------ EDIT----------------------- My sprite sheet. Consider the animation from Left to right and then from top to bottom Here is an image for a better understanding. My spritesheet ... class FragileSquare{ FloatBuffer fVertexBuffer, mTextureBuffer; ByteBuffer mColorBuff; ByteBuffer mIndexBuff; int[] textures = new int[1]; public boolean beingHitFromBall = false; int numberSprites = 20; int columnInt = 4; //number of columns as int float columnFloat = 4.0f; //number of columns as float float rowFloat = 5.0f; int oldIdx; public FragileSquare() { // TODO Auto-generated constructor stub float vertices [] = {-1.0f,1.0f, //byte index 0 1.0f, 1.0f, //byte index 1 //byte index 2 -1.0f, -1.0f, 1.0f,-1.0f}; //byte index 3 float textureCoord[] = { 0.0f,0.0f, 0.25f,0.0f, 0.0f,0.20f, 0.25f,0.20f }; byte indices[] = {0, 1, 2, 1, 2, 3 }; ByteBuffer byteBuffer = ByteBuffer.allocateDirect(4*2 * 4); // 4 vertices, 2 co-ordinates(x,y) 4 for converting in float byteBuffer.order(ByteOrder.nativeOrder()); fVertexBuffer = byteBuffer.asFloatBuffer(); fVertexBuffer.put(vertices); fVertexBuffer.position(0); ByteBuffer byteBuffer2 = ByteBuffer.allocateDirect(textureCoord.length * 4); byteBuffer2.order(ByteOrder.nativeOrder()); mTextureBuffer = byteBuffer2.asFloatBuffer(); mTextureBuffer.put(textureCoord); mTextureBuffer.position(0); } public void draw(GL10 gl){ gl.glFrontFace(GL11.GL_CW); gl.glEnableClientState(GL10.GL_VERTEX_ARRAY); gl.glVertexPointer(1,GL10.GL_FLOAT, 0, fVertexBuffer); gl.glEnable(GL10.GL_TEXTURE_2D); if(MyRender.flag2==1){ /** Collision has taken place*/ int idx = oldIdx==(numberSprites-1) ? (numberSprites-1) : (int)((System.currentTimeMillis()%(200*numberSprites))/200); gl.glMatrixMode(GL10.GL_TEXTURE); gl.glTranslatef((idx%columnInt)/columnFloat, (idx/columnInt)/rowFloat, 0); gl.glMatrixMode(GL10.GL_MODELVIEW); oldIdx = idx; } gl.glEnable(GL10.GL_BLEND); gl.glBlendFunc(GL10.GL_SRC_ALPHA, GL10.GL_ONE_MINUS_SRC_ALPHA); gl.glBindTexture(GL10.GL_TEXTURE_2D, textures[0]); //4 gl.glTexCoordPointer(2, GL10.GL_FLOAT,0, mTextureBuffer); //5 gl.glEnableClientState(GL10.GL_TEXTURE_COORD_ARRAY); gl.glDrawArrays(GL10.GL_TRIANGLE_STRIP, 0, 4); //7 gl.glFrontFace(GL11.GL_CCW); gl.glDisableClientState(GL10.GL_VERTEX_ARRAY); gl.glDisableClientState(GL10.GL_TEXTURE_COORD_ARRAY); gl.glMatrixMode(GL10.GL_TEXTURE); gl.glLoadIdentity(); gl.glMatrixMode(GL10.GL_MODELVIEW); } public void loadFragileTexture(GL10 gl, Context context, int resource) { Bitmap bitmap = BitmapFactory.decodeResource(context.getResources(), resource); gl.glGenTextures(1, textures, 0); gl.glBindTexture(GL10.GL_TEXTURE_2D, textures[0]); gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MIN_FILTER, GL10.GL_LINEAR); gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_MAG_FILTER, GL10.GL_LINEAR); gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_WRAP_S, GL10.GL_REPEAT); gl.glTexParameterf(GL10.GL_TEXTURE_2D, GL10.GL_TEXTURE_WRAP_T, GL10.GL_REPEAT); GLUtils.texImage2D(GL10.GL_TEXTURE_2D, 0, bitmap, 0); bitmap.recycle(); }

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• Help me get my 3D camera to look like the ones in RTS

  - by rFactor

  I am a newbie in 3D game development and I am trying to make a real-time strategy game. I am struggling with the camera currently as I am unable to make it look like they do in RTS games. Here is my Camera.cs class using System; using System.Collections.Generic; using System.Linq; using System.Text; using Microsoft.Xna.Framework; using Microsoft.Xna.Framework.Input; namespace BB { public class Camera : Microsoft.Xna.Framework.GameComponent { public Matrix view; public Matrix projection; protected Game game; KeyboardState currentKeyboardState; Vector3 cameraPosition = new Vector3(600.0f, 0.0f, 600.0f); Vector3 cameraForward = new Vector3(0, -0.4472136f, -0.8944272f); BoundingFrustum cameraFrustum = new BoundingFrustum(Matrix.Identity); // Light direction Vector3 lightDir = new Vector3(-0.3333333f, 0.6666667f, 0.6666667f); public Camera(Game game) : base(game) { this.game = game; } public override void Initialize() { this.view = Matrix.CreateLookAt(this.cameraPosition, this.cameraPosition + this.cameraForward, Vector3.Up); this.projection = Matrix.CreatePerspectiveFieldOfView(MathHelper.PiOver4, this.game.renderer.aspectRatio, 1, 10000); base.Initialize(); } /* Handles the user input * @ param GameTime gameTime */ private void HandleInput(GameTime gameTime) { float time = (float)gameTime.ElapsedGameTime.TotalMilliseconds; currentKeyboardState = Keyboard.GetState(); } void UpdateCamera(GameTime gameTime) { float time = (float)gameTime.ElapsedGameTime.TotalMilliseconds; // Check for input to rotate the camera. float pitch = 0.0f; float turn = 0.0f; if (currentKeyboardState.IsKeyDown(Keys.Up)) pitch += time * 0.001f; if (currentKeyboardState.IsKeyDown(Keys.Down)) pitch -= time * 0.001f; if (currentKeyboardState.IsKeyDown(Keys.Left)) turn += time * 0.001f; if (currentKeyboardState.IsKeyDown(Keys.Right)) turn -= time * 0.001f; Vector3 cameraRight = Vector3.Cross(Vector3.Up, cameraForward); Vector3 flatFront = Vector3.Cross(cameraRight, Vector3.Up); Matrix pitchMatrix = Matrix.CreateFromAxisAngle(cameraRight, pitch); Matrix turnMatrix = Matrix.CreateFromAxisAngle(Vector3.Up, turn); Vector3 tiltedFront = Vector3.TransformNormal(cameraForward, pitchMatrix * turnMatrix); // Check angle so we cant flip over if (Vector3.Dot(tiltedFront, flatFront) > 0.001f) { cameraForward = Vector3.Normalize(tiltedFront); } // Check for input to move the camera around. if (currentKeyboardState.IsKeyDown(Keys.W)) cameraPosition += cameraForward * time * 0.4f; if (currentKeyboardState.IsKeyDown(Keys.S)) cameraPosition -= cameraForward * time * 0.4f; if (currentKeyboardState.IsKeyDown(Keys.A)) cameraPosition += cameraRight * time * 0.4f; if (currentKeyboardState.IsKeyDown(Keys.D)) cameraPosition -= cameraRight * time * 0.4f; if (currentKeyboardState.IsKeyDown(Keys.R)) { cameraPosition = new Vector3(0, 50, 50); cameraForward = new Vector3(0, 0, -1); } cameraForward.Normalize(); // Create the new view matrix view = Matrix.CreateLookAt(cameraPosition, cameraPosition + cameraForward, Vector3.Up); // Set the new frustum value cameraFrustum.Matrix = view * projection; } public override void Update(Microsoft.Xna.Framework.GameTime gameTime) { HandleInput(gameTime); UpdateCamera(gameTime); } } } The problem is that the initial view is looking in a horizontal direction. I would like to have an RTS like top down view (but with a slight pitch). Can you help me out?

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• Problems implementing a screen space shadow ray tracing shader

  - by Grieverheart

  Here I previously asked for the possibility of ray tracing shadows in screen space in a deferred shader. Several problems were pointed out. One of the most important problem is that only visible objects can cast shadows and objects between the camera and the shadow caster can interfere. Still I thought it'd be a fun experiment. The idea is to calculate the view coordinates of pixels and cast a ray to the light. The ray is then traced pixel by pixel to the light and its depth is compared with the depth at the pixel. If a pixel is in front of the ray, a shadow is casted at the original pixel. At first I thought that I could use the DDA algorithm in 2D to calculate the distance 't' (in p = o + t d, where o origin, d direction) to the next pixel and use it in the 3D ray equation to find the ray's z coordinate at that pixel's position. For the 2D ray, I would use the projected and biased 3D ray direction and origin. The idea was that 't' would be the same in both 2D and 3D equations. Unfortunately, this is not the case since the projection matrix is 4D. Thus, some tweak needs to be done to make this work this way. I would like to ask if someone knows of a way to do what I described above, i.e. from a 2D ray in texture coordinate space to get the 3D ray in screen space. I did implement a simple version of the idea which you can see in the following video: video here Shadows may seem a bit pixelated, but that's mostly because of the size of the step in 't' I chose. And here is the shader: #version 330 core uniform sampler2D DepthMap; uniform vec2 projAB; uniform mat4 projectionMatrix; const vec3 light_p = vec3(-30.0, 30.0, -10.0); noperspective in vec2 pass_TexCoord; smooth in vec3 viewRay; layout(location = 0) out float out_AO; vec3 CalcPosition(void){ float depth = texture(DepthMap, pass_TexCoord).r; float linearDepth = projAB.y / (depth - projAB.x); vec3 ray = normalize(viewRay); ray = ray / ray.z; return linearDepth * ray; } void main(void){ vec3 origin = CalcPosition(); if(origin.z < -60) discard; vec2 pixOrigin = pass_TexCoord; //tex coords vec3 dir = normalize(light_p - origin); vec2 texel_size = vec2(1.0 / 600.0); float t = 0.1; ivec2 pixIndex = ivec2(pixOrigin / texel_size); out_AO = 1.0; while(true){ vec3 ray = origin + t * dir; vec4 temp = projectionMatrix * vec4(ray, 1.0); vec2 texCoord = (temp.xy / temp.w) * 0.5 + 0.5; ivec2 newIndex = ivec2(texCoord / texel_size); if(newIndex != pixIndex){ float depth = texture(DepthMap, texCoord).r; float linearDepth = projAB.y / (depth - projAB.x); if(linearDepth > ray.z + 0.1){ out_AO = 0.2; break; } pixIndex = newIndex; } t += 0.5; if(texCoord.x < 0 || texCoord.x > 1.0 || texCoord.y < 0 || texCoord.y > 1.0) break; } } As you can see, here I just increment 't' by some arbitrary factor, calculate the 3D ray and project it to get the pixel coordinates, which is not really optimal. Hopefully, I would like to optimize the code as much as possible and compare it with shadow mapping and how it scales with the number of lights. PS: Keep in mind that I reconstruct position from depth by interpolating rays through a full screen quad.

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• Problems with moving 2D circle/box collision detection

  - by dario3004

  This is my first game ever and I'm a newbie in computer physics. I've got this code for the collision detection and it works fine for BOTTOM and TOP collision.It miss the collision detection with the paddle's edge and angles so I've (roughly) tried to implement it. Main method that is called for bouncing, it checks if it bounce with wall, or with top (+ right/left side) or with bottom (+ right/left side): protected void handleBounces(float px, float py) { handleWallBounce(px, py); if(mBall.y < getHeight()/4){ if (handleRedFastBounce(mRed, px, py)) return; if (handleRightSideBounce(mRed,px,py)) return; if (handleLeftSideBounce(mRed,px,py)) return; } if(mBall.y > getHeight()/4 * 3){ if (handleBlueFastBounce(mBlue, px, py)) return; if (handleRightSideBounce(mBlue,px,py)) return; if (handleLeftSideBounce(mBlue,px,py)) return; } } This is the code for the BOTTOM bounce: protected boolean handleRedFastBounce(Paddle paddle, float px, float py) { if (mBall.goingUp() == false) return false; // next position tx = mBall.x; ty = mBall.y - mBall.getRadius(); // actual position ptx = px; pty = py - mBall.getRadius(); dyp = ty - paddle.getBottom(); xc = tx + (tx - ptx) * dyp / (ty - pty); if ((ty < paddle.getBottom() && pty > paddle.getBottom() && xc > paddle.getLeft() && xc < paddle.getRight())) { mBall.x = xc; mBall.y = paddle.getBottom() + mBall.getRadius(); mBall.bouncePaddle(paddle); playSound(mPaddleSFX); increaseDifficulty(); return true; } else return false; } As long as I understood it should be something like this: So I tried to make the "left side" and "right side" bounce method: protected boolean handleLeftSideBounce(Paddle paddle, float px, float py){ // next position tx = mBall.x + mBall.getRadius(); ty = mBall.y; // actual position ptx = px + mBall.getRadius(); pty = py; dyp = tx - paddle.getLeft(); yc = ty + (pty - ty) * dyp / (ptx - tx); if (ptx < paddle.getLeft() && tx > paddle.getLeft()){ System.out.println("left side bounce1"); System.out.println("yc: " + yc + "top: " + paddle.getTop() + " bottom: " + paddle.getBottom()); if (yc > paddle.getTop() && yc < paddle.getBottom()){ System.out.println("left side bounce2"); mBall.y = yc; mBall.x = paddle.getLeft() - mBall.getRadius(); mBall.bouncePaddle(paddle); playSound(mPaddleSFX); increaseDifficulty(); return true; } } return false; } I think I'm quite near to the solution but I'm having big troubles with the new "yc" formula. I tried so many versions of it but since I don't know the theory behind it I can't adjust for the Y axis. Since the Y axis is inverted I even tried this: yc = ty - (pty - ty) * dyp / (ptx - tx); I tried Googling it but I can't seem to find a solution for it. Also this method fails when ball touches the angle and I don't think is a nice way because it just test "one" point of the ball and probably there will be many cases in which the ball won't bounce.

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• Detect multitouch (two fingers touch) on a sprite to apply pinch zoom behaviour

  - by Tahreem

  I am using andengine, want to move, zoom and rotate multiple sprites individually on a scene. I have achieved "move" but for pinch zoom i am unable to get the event to two fingers' touch. Below is the code: public class Main extends SimpleBaseGameActivity { private Camera camera; private BitmapTextureAtlas mBitmapTextureAtlas; private ITextureRegion mFaceTextureRegion; private ITextureRegion mFaceTextureRegion2; Sprite face2; private static final int CAMERA_WIDTH = 800; private static final int CAMERA_HEIGHT = 480; @Override public EngineOptions onCreateEngineOptions() { camera = new Camera(0, 0, CAMERA_WIDTH, CAMERA_HEIGHT); EngineOptions engineOptions = new EngineOptions(true, ScreenOrientation.LANDSCAPE_FIXED, new RatioResolutionPolicy( CAMERA_WIDTH, CAMERA_HEIGHT), camera); return engineOptions; } @Override protected void onCreateResources() { BitmapTextureAtlasTextureRegionFactory.setAssetBasePath("gfx/"); this.mBitmapTextureAtlas = new BitmapTextureAtlas( this.getTextureManager(), 1024, 1600, TextureOptions.NEAREST); BitmapTextureAtlasTextureRegionFactory.createTiledFromAsset(this.mBitmapTextureAtlas, // this, "ui_ball_1.png", 0, 0, 1, 1), // this.getVertexBufferObjectManager()); this.mFaceTextureRegion = BitmapTextureAtlasTextureRegionFactory .createFromAsset(this.mBitmapTextureAtlas, this, "ui_ball_1.png", 0, 0); this.mFaceTextureRegion2 = BitmapTextureAtlasTextureRegionFactory .createFromAsset(this.mBitmapTextureAtlas, this, "ui_ball_1.png", 0, 0); this.mBitmapTextureAtlas.load(); this.mEngine.getTextureManager().loadTexture(this.mBitmapTextureAtlas); } @Override protected Scene onCreateScene() { this.mEngine.registerUpdateHandler(new FPSLogger()); final Scene scene = new Scene(); scene.setBackground(new Background(0.09804f, 0.6274f, 0.8784f)); final float centerX = (CAMERA_WIDTH - this.mFaceTextureRegion .getWidth()) / 2; final float centerY = (CAMERA_HEIGHT - this.mFaceTextureRegion .getHeight()) / 2; final Sprite face = new Sprite(centerX, centerY, this.mFaceTextureRegion, this.getVertexBufferObjectManager()) { @Override public boolean onAreaTouched(final TouchEvent pSceneTouchEvent, final float pTouchAreaLocalX, final float pTouchAreaLocalY) { this.setPosition(pSceneTouchEvent.getX() - this.getWidth() / 2, pSceneTouchEvent.getY() - this.getHeight() / 2); return true; } }; face.setScale(2); scene.attachChild(face); scene.registerTouchArea(face); face2 = new Sprite(200, 200, this.mFaceTextureRegion2, this.getVertexBufferObjectManager()) { @Override public boolean onAreaTouched(final TouchEvent pSceneTouchEvent, final float pTouchAreaLocalX, final float pTouchAreaLocalY) { switch(pSceneTouchEvent.getAction()){ case TouchEvent.ACTION_DOWN: int count = pSceneTouchEvent.getMotionEvent().getPointerCount() ; for(int i= 0; i <count; i++) { int id = pSceneTouchEvent.getMotionEvent().getPointerId(i); } break; case TouchEvent.ACTION_MOVE: this.setPosition(pSceneTouchEvent.getX() -this.getWidth() / 2, pSceneTouchEvent.getY()-this.getHeight() / 2); break; case TouchEvent.ACTION_UP: break; } return true; } }; face2.setScale(2); scene.attachChild(face2); scene.registerTouchArea(face2); scene.setTouchAreaBindingOnActionDownEnabled(true); return scene; } } This line int count = pSceneTouchEvent.getMotionEvent().getPointerCount() ; should set 2 to the count variable if i touch the sprite with to fingers, then i can apply zooming functionality (setScale method) on the sprite by getting the distance between the coordinates of two fingers. Can anyone help me? why it does not detect two fingers? and without this how can i zoom the sprite on pinch of two fingers? I am very new to game development, any help would be appreciated. Thanks in advance.

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• Resolving collisions between dynamic game objects

  - by TheBroodian

  I've been building a 2D platformer for some time now, I'm getting to the point where I am adding dynamic objects to the stage for testing. This has prompted me to consider how I would like my character and other objects to behave when they collide. A typical staple in many 2D platformer type games is that the player takes damage upon touching an enemy, and then essentially becomes able to pass through enemies during a period of invulnerability, and at the same time, enemies are able to pass through eachother freely. I personally don't want to take this approach, it feels strange to me that the player should receive arbitrary damage for harmless contact to an enemy, despite whether the enemy is attacking or not, and I would like my enemies' interactions between each other (and my player) to be a little more organic, so to speak. In my head I sort of have this idea where a game object (player, or non player) would be able to push other game objects around by manner of 'pushing' each other out of one anothers' bounding boxes if there is an intersection, and maybe correlate the repelling force to how much their bounding boxes are intersecting. The problem I'm experiencing is I have no idea what the math might look like for something like this? I'll show what work I've done so far, it sort of works, but it's jittery, and generally not quite what I would pass in a functional game: //Clears the anti-duplicate buffer collisionRecord.Clear(); //pick a thing foreach (GameObject entity in entities) { //pick another thing foreach (GameObject subject in entities) { //check to make sure both things aren't the same thing if (!ReferenceEquals(entity, subject)) { //check to see if thing2 is in semi-near proximity to thing1 if (entity.WideProximityArea.Intersects(subject.CollisionRectangle) || entity.WideProximityArea.Contains(subject.CollisionRectangle)) { //check to see if thing2 and thing1 are colliding. if (entity.CollisionRectangle.Intersects(subject.CollisionRectangle) || entity.CollisionRectangle.Contains(subject.CollisionRectangle) || subject.CollisionRectangle.Contains(entity.CollisionRectangle)) { //check if we've already resolved their collision or not. if (!collisionRecord.ContainsKey(entity.GetHashCode())) { //more duplicate resolution checking. if (!collisionRecord.ContainsKey(subject.GetHashCode())) { //if thing1 is traveling right... if (entity.Velocity.X > 0) { //if it isn't too far to the right... if (subject.CollisionRectangle.Contains(new Microsoft.Xna.Framework.Rectangle(entity.CollisionRectangle.Right, entity.CollisionRectangle.Y, 1, entity.CollisionRectangle.Height)) || subject.CollisionRectangle.Intersects(new Microsoft.Xna.Framework.Rectangle(entity.CollisionRectangle.Right, entity.CollisionRectangle.Y, 1, entity.CollisionRectangle.Height))) { //Find how deep thing1 is intersecting thing2's collision box; float offset = entity.CollisionRectangle.Right - subject.CollisionRectangle.Left; //Move both things in opposite directions half the length of the intersection, pushing thing1 to the left, and thing2 to the right. entity.Velocities.Add(new Vector2(-(((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); subject.Velocities.Add(new Vector2((((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); } } //if thing1 is traveling left... if (entity.Velocity.X < 0) { //if thing1 isn't too far left... if (entity.CollisionRectangle.Contains(new Microsoft.Xna.Framework.Rectangle(subject.CollisionRectangle.Right, subject.CollisionRectangle.Y, 1, subject.CollisionRectangle.Height)) || entity.CollisionRectangle.Intersects(new Microsoft.Xna.Framework.Rectangle(subject.CollisionRectangle.Right, subject.CollisionRectangle.Y, 1, subject.CollisionRectangle.Height))) { //Find how deep thing1 is intersecting thing2's collision box; float offset = subject.CollisionRectangle.Right - entity.CollisionRectangle.Left; //Move both things in opposite directions half the length of the intersection, pushing thing1 to the right, and thing2 to the left. entity.Velocities.Add(new Vector2((((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); subject.Velocities.Add(new Vector2(-(((offset * 4) * (float)gameTime.ElapsedGameTime.TotalMilliseconds)), 0)); } } //Make record that thing1 and thing2 have interacted and the collision has been solved, so that if thing2 is picked next in the foreach loop, it isn't checked against thing1 a second time before the next update. collisionRecord.Add(entity.GetHashCode(), subject.GetHashCode()); } } } } } } } } One of the biggest issues with my code aside from the jitteriness is that if one character were to land on top of another character, it very suddenly and abruptly resolves the collision, whereas I would like a more subtle and gradual resolution. Any thoughts or ideas are incredibly welcome and helpful.

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